File:2x2chart110602.pdf

English: 2 X 2 Games: Visualizing the Adjacent Possible in the Topology of Two-player, Two-strategy Games. Alternative visualizations of the topology of 2x2 ordinal games, based on the topology developed by David Robinson and David Goforth, as presented in their book The Topology of 2x2 Games: A New Periodic Table, and their periodic table of ordinal 2x2 games, available at: www.cs.laurentian.ca/dgoforth/home.html. This visualization includes a numeric display of game payoffs, introductory overview, diagrams illustrating the structure of the topology, and an alternative version with order graphs. The topology shows how swaps in adjoining payoffs transform games, for example swapping the two lowest-ranked payoffs to change Prisoner's Dilemma into a game of Chicken. Further swaps link Battle of the Sexes, Prisoner's Delight, Stag Hunt, Assurance, Coordination, Harmony, Samaritan's Dilemma, and all other two-player, two-move strict ordinal games (four ranked payoffs, no ties). The topology shows how games can be transformed into each other, including changing social dilemmas into win-win games. Source files available from the author on request.